Maharsha in Hiddushei Aggadot to Kiddushin (40b) explains the correlation of one who eats on the street to a dog is in that a dog does not have his food at home and therefore goes searching for bits of food here and there eating a drop here and a drop there.
This coincides with the common phrase 'he is eating like a hungry dog' this being the result of him not having food in his dwelling place.
Chewing gum is a habit of someone eager, hungered, agitated and unsettled.Someone who shamelessly portrays himself as hungry(לא רעב ללחם not hungry for bread but hungry nevertheless) and as admitting a gap is not fit to be a witness.
This may be somewhat comparable to the concept we find C'M' 263' when considering picking up something on the street, for instance, to return it to its rightful owner, that depending on the person somethings may be too insignificant to have someone important(Talmud Chochom) picking it up and he, if important, shall not be obliged to pick it up.
Considering chewing gum on the street, is shameful as for such an insignificant food one is embarrassing himself in public.For had it been something significant at least it may be worth embarrassing oneself for that.
Rav Avigdor Miller is quoted telling someone, upon seen eating on the street arguing that he is eating something small, that 'if so you are a puppy'.
All this is in accordance with the understanding of Rashi in Kidushin as well as the last peshat in tosafot in Kidushin that the problem with this man is his eating on the street which is the understanding of the Rambam le'halacha ,however Tosafot provides us with an all other understanding of the halacha and that is that the issue here is one of stealing and grabbing from another.More than that, even if the issue is one of eating on the street it is still uncertain whether or not the halacha pertains to someone eating a snack rather than a meal.Nevertheless, the facts as put on the table call for us to be careful with that as being a sofek posul le'edut and a sofek not being min ha'yishuv meaning people contributing to society is not rewarding.
Dibros Moshe on that gemarah points out that you derive from here that one need be embarrassed to be a posul le'eidut, as that is the reasoning behind this pesul.Once again we see the importance in being scrupulous in this manner as careful as one is retain his simole dignity.
I may add that being embarrssed is from the signs of a jew and is from his essence and is a result of yiras Hashem as the gemorah states regarding the posuk in Yitro ובעבור תהיה יראתו על פניכם לבלתי תחטאו.
Therefore it is an utmost significant affair to be concerned about.
Its worth noting that the Bach in C'M' 34' says that unlike what the Bais Yosef says even when there are only a few people walking the streets he is nevertheless rendered posul le'edut as it is a place that Rabim Bokim Bo meaning it's meant for and designated for public walking.Seemingly this would a regular street even not a marketplace. See the yaavets in the back of the Gemarah that states clearly that it may even be in a chatser which people would refrain from eating therein being there are people going around there.